Approaches for identifying U.S. medicare fraud in provider claims data

Abstract

Quality and affordable healthcare is an important aspect in people’s lives, particularly as they age. The rising elderly population in the United States (U.S.), with increasing number of chronic diseases, implies continuing healthcare later in life and the need for programs, such as U.S. Medicare, to help with associated medical expenses. Unfortunately, due to healthcare fraud, these programs are being adversely affected draining resources and reducing quality and accessibility of necessary healthcare services. The detection of fraud is critical in being able to identify and, subsequently, stop these perpetrators. The application of machine learning methods and data mining strategies can be leveraged to improve current fraud detection processes and reduce the resources needed to find and investigate possible fraudulent activities. In this paper, we employ an approach to predict a physician’s expected specialty based on the type and number of procedures performed. From this approach, we generate a baseline model, comparing Logistic Regression and Multinomial Naive Bayes, in order to test and assess several new approaches to improve the detection of U.S. Medicare Part B provider fraud. Our results indicate that our proposed improvement strategies (specialty grouping, class removal, and class isolation), applied to different medical specialties, have mixed results over the selected Logistic Regression baseline model’s fraud detection performance. Through our work, we demonstrate that improvements to current detection methods can be effective in identifying potential fraud.

Appendices

Appendix A

Multinomial Naive Bayes classifies new instances, in our case these instances consist of new Medicare claims per year for a particular provider, by finding the posterior probabilities of class membership based on each feature value, which is learned from a set of labeled training instances. The approximation is done using Bayes’ rule by assuming conditional independence. Conditional independence is the idea that each feature in the dataset is independent from one another which is rarely true in practice, however, the model is very effective and is used extensively in the field of data mining and machine learning [33]. Naive Bayes is used with both PySpark and Weka.

Logistic Regression predicts probabilities for which class a categorically distributed dependent variable belongs to by using a set of independent variables employing a logistic function. Multinomial Logistic Regression (MLR) is an extension of binomial Logistic Regression that allows for more than two categories of the dependent variable. Unlike Naive Bayes, there is no requirement for statistical independence between independent variables, though there is an assumption of collinearity [40, 41]. We used Logistic Regression in both Weka and PySpark. Logistic Regression with the Limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm (LBFGS) is the version used in our study to improve memory usage [42]. In this research, we will be using data for both binomial and mulitnomial Logistic Regression.

Support Vector Machine models create a space consisting of training instances portraying them as points, mapping them in a way that best creates linearly separable categories, where the goal is to have the largest gap between them. The specific implementation of SVM used in Weka is called Sequential Minimal Optimization (SMO), which uses this optimization algorithm as the training method for Support Vector Classification [40, 43].

Random Forest is an ensemble learning method that generates a large number of trees. The class value that appears most often among these trees, or mode, is the class predicted as output from the model. As an ensemble learning method, RF is an aggregation of various tree predictors where each tree within the forest is dependent upon the values dictated by a random vector that is independently sampled [40, 44]. We use the Random Forest learner only in Weka.

Appendix B

Type I error rate (false positive rate) is the percentage of instances that are actually non-fraud but marked as fraud, in relation to the number of actual non-fraud instances. A fire alarm going off indicating a fire when in fact there is no fire would be an example of this kind of error. Type II error rate (false negative rate) is the percentage of instances that are actually fraud but marked as non-fraud, in relation to the actual number of actual fraud instances. As an example, a fire breaking out and the fire alarm does not ring would be considered a false negative. Note that in binary classification, finding a balance between the error rates, while minimizing the Type II error rate, is generally preferred. Recall measures the ability of a classifier to determine the rate of positively marked instances that are in fact positive; therefore, in our study, recall is the fraction of physicians labeled correctly and not as any of the other specialties. Precision indicates how well a classifier has predicted a class by finding the ratio of actually positive instances from the pool of instances that it has marked as part of the positive class; therefore, precision shows the fraction of physicians marked correctly against the number of physicians, from any of the other specialties, also marked as the class in question.

F-score (also known as F1-score or F-measure) is the harmonic mean of both precision and recall, generating a number between 0 and 1, where values closer to one indicate better performance. For this study, we assume equal weighting between precision and recall, with β = 1, as seen in Eq. 1.

$$ F_{1} = (1 + \beta^{2}) \times \frac{Recall \times Precision}{(\beta^{2} \times Recall) + Precision} $$

(1)

G-measure, also known as the Fowlkes-Mallows index, gives the geometric mean of precision and recall giving the central point between the values as seen in Eq. 2.

$$ \text{G-measure} = \sqrt{Recall \times Precision} $$

(2)

Finally, in order to leverage the successes from our prior works, we manipulated the datasets, by filtering out certain specialties only, so that we could test one fraudulent specialty at a time (based on the model predicting the physician’s specialty). Since the test dataset contains only one specialty at a time, the overall accuracy would be the percentage of real-world fraudulent physicians that are considered not fraudulent. In order to capture the the percentages of classes that are labeled as another class, we incorporate the Inverse Overall Accuracy (IOA) performance measure. IOA, where IOA = 1 −overall accuracy, is the percentage of fraudulent physicians marked as fraudulent for a given specialty. As shown in Eq. 3, to calculate the model’s overall weighted average IOA (owaIOA), we take the IOA for a specialty, the number of fraudulent instances (n) for that specialty and the total number of instances (N), and sum over the total number of fraudulent instances between all specialties with F-score of 0.75 or above (NoS).

$$ owaIOA = \sum\limits_{i = 1}^{i=NoS} \frac{n_{i}}{N} \times IOA_{i} $$

(3)

Appendix C

Table 15 Fraud detection results with groups only (group test one)

Table 16 Fraud detection results with groups and non-grouped specialties (group test two)

Table 17 Class removal (original four classes) fraud detection results

Table 18 Class removal (chosen classes) fraud detection results